Unified analysis of periodization-based sampling methods for matérn covariances
The periodization of a stationary Gaussian random field on a sufficiently large torus comprising the spatial domain of interest is the basis of various efficient computational methods, such as the classical circulant embedding technique using the fast Fourier transform for generating samples on unif...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
20 October 2020
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| In: |
SIAM journal on numerical analysis
Year: 2020, Volume: 58, Issue: 5, Pages: 2953-2980 |
| ISSN: | 1095-7170 |
| DOI: | 10.1137/19M1269877 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1137/19M1269877 Verlag, lizenzpflichtig, Volltext: https://epubs.siam.org/doi/10.1137/19M1269877 
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| Author Notes: | Markus Bachmayr, Ivan G. Graham, Van Kien Nguyen, and Robert Scheichl |
| Summary: | The periodization of a stationary Gaussian random field on a sufficiently large torus comprising the spatial domain of interest is the basis of various efficient computational methods, such as the classical circulant embedding technique using the fast Fourier transform for generating samples on uniform grids. For the family of Matérn covariances with smoothness index $\nu$ and correlation length $\lambda$, we analyze the nonsmooth periodization (corresponding to classical circulant embedding) and an alternative procedure using a smooth truncation of the covariance function. We solve two open problems: the first concerning the $\nu$-dependent asymptotic decay of eigenvalues of the resulting circulant in the nonsmooth case, the second concerning the required size in terms of $\nu$, $\lambda$ of the torus when using a smooth periodization. In doing this we arrive at a complete characterization of the performance of these two approaches. Both our theoretical estimates and the numerical tests provided here show substantial advantages of smooth truncation. |
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| Item Description: | Gesehen am 02.02.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1095-7170 |
| DOI: | 10.1137/19M1269877 |